Question

The ratio of the velocity of the hydrogen molecule to that of the oxygen molecule under identical conditions is:

• A. 1:4
• B. 4:1
• C. 1:16
• D. 16:1

Hint:

Lighter molecules move faster! Since Hydrogen is 16 times lighter than Oxygen, its velocity is $\sqrt{16} = 4$ times greater.

Answer 1

The Correct Option is B

Step 1: Concept
According to Graham's Law of Effusion, the velocity ($v$) of a gas is inversely proportional to the square root of its molar mass ($M$): $v \propto \frac{1}{\sqrt{M}}$.

Step 2: Meaning
Molar mass of $H_2 = 2$ g/mol. Molar mass of $O_2 = 32$ g/mol.

Step 3: Analysis
The ratio is calculated as: $$\frac{v_{H2}}{v_{O2}} = \sqrt{\frac{M_{O2}}{M_{H2}}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4$$ This results in a ratio of 4:1.

Step 4: Conclusion
Since Hydrogen is much lighter, it moves faster than Oxygen. The ratio of their velocities is 4:1. Final Answer: (B)